Question

Solve the below equation with fraction coefficients.

$\frac{3}{4}x-\frac{1}{2}=\frac{1}{4}$

Short answer

The solution is$x=1$.

Step-by-step solution

Step 1. Given information.

The given equation is$\frac{3}{4}x-\frac{1}{2}=\frac{1}{4}$.

Step 2. Find the least common denominator of all fractions in the given equation.

We know that the LCM of denominators $4,2,4$is $4$.

So, the LCD of all fractions given in the equation$\frac{1}{4},\frac{1}{2},\frac{3}{4}$is$4$.

Step 3. Multiply both sides of the equation with LCD.

Multiply both the side by $4$.

$$\begin{gathered} 4\left(\frac{3}{4}x-\frac{1}{2}\right)=4\left(\frac{1}{4}\right) \\ 4\times \frac{3}{4}x-4\times \frac{1}{2}=4\times \frac{1}{4} \\ 3x-2=1 \end{gathered}$$

Step 4. Simplify the above equation.

Add $2$on both sides.

$$\begin{gathered} 3x-2+2=1+2 \\ 3x=3 \end{gathered}$$

Divide each side by $3$.

$$\begin{gathered} \frac{3x}{3}=\frac{3}{3} \\ x=1 \end{gathered}$$

Hence, the solution of the given equation is$x=1$.